While large language models (LLMs) excel in many domains, their complexity and scale challenge deployment in resource-limited environments. Current compression techniques, such as parameter pruning, often fail to effectively utilize the knowledge from pruned parameters. To address these challenges, we propose Manifold-Based Knowledge Alignment and Layer Merging Compression (MKA), a novel approach that uses manifold learning and the Information Bottleneck (IB) measure to merge similar layers, reducing model size while preserving essential performance. We evaluate MKA on multiple benchmark datasets and various LLMs. Our findings show that MKA not only preserves model performance but also achieves substantial compression ratios, outperforming traditional pruning methods. Moreover, when coupled with quantization, MKA delivers even greater compression. Specifically, on the MMLU dataset using the Llama3-8B model, MKA achieves a compression ratio of 43.75% with a minimal performance decrease of only 2.82%. The proposed MKA method offers a resource-efficient and performance-preserving model compression technique for LLMs. We make our code available at https://github.com/SempraETY/Pruning-via-Merging

Chain-of-Thought (CoT) prompting combined with large language models (LLM) has shown great potential in improving performance on challenging reasoning tasks. While understanding why CoT prompting is effective is crucial for the application and improvement of CoT prompting, few studies have addressed this issue. Besides, almost no prior work has conducted theoretical analysis on CoT prompting in the context of black-box models. In this paper, we approach the analysis of CoT prompting in black-box LLMs from an information-theoretic perspective. Specifically, we propose a new metric, EPVI (Estimated Pointwise V-Information), which extends the concept of pointwise V-information to black-box models, quantifying the label-relevant new information introduced by CoT prompting beyond the pre-existing information in the input. Based on this, we conduct a series of experiments at both the task and instance levels to analyze CoT prompting, demonstrating that the effectiveness of CoT prompting can be attributed to its capacity to influence the difficulty of model inference by augmenting or reducing the model-usable information. Furthermore, we show that selecting high-quality demonstrations of CoT reasoning based on EPVI can improve the downstream performance of reasoning tasks.